Problem Statement

There are N people whose IDs are 1, 2, \ldots, and N.

Each of person 1, person 2, \ldots, and person N performs the following action once in this order:

• If person i's ID has not been called out yet, call out person A_i's ID.

Enumerate the IDs of all the people whose IDs are never called out until the end in ascending order.

Constraints

• 2 \leq N \leq 2 \times 10^5
• 1 \leq A_i \leq N
• A_i \neq i
• All values in the input are integers.

Sample Input 1

5
3 1 4 5 4

Sample Output 1

2
2 4

The five people's actions are as follows.

• Person 1's ID has not been called out yet, so person 1 calls out person 3's ID.
• Person 2's ID has not been called out yet, so person 2 calls out person 1's ID.
• Person 3's ID has already been called out by person 1, so nothing happens.
• Person 4's ID has not been called out yet, so person 4 calls out person 5's ID.
• Person 5's ID has already been called out by person 4, so nothing happens.

Therefore, person 2 and 4's IDs are not called out until the end.

Sample Input 2

20
9 7 19 7 10 4 13 9 4 8 10 15 16 3 18 19 12 13 2 12

Sample Output 2

10
1 2 5 6 8 11 14 17 18 20

Problem Statement

You are given N strings, each of length 2, consisting of uppercase English letters and digits. The i-th string is S_i.
Determine whether the following three conditions are all satisfied.
・For every string, the first character is one of H, D, C, and S.
・For every string, the second character is one of A, 2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K.
・All strings are pairwise different. That is, if i \neq j, then S_i \neq S_j.

Constraints

• 1 \leq N \leq 52
• S_i is a string of length 2 consisting of uppercase English letters and digits.

Sample Input 1

4
H3
DA
D3
SK

Sample Output 1

Yes

One can verify that the three conditions are all satisfied.

Sample Input 2

5
H3
DA
CK
H3
S7

Sample Output 2

No

Both S_1 and S_4 are H3, violating the third condition.

Sample Input 3

4
3H
AD
3D
KS

Sample Output 3

No

Sample Input 4

5
00
AA
XX
YY
ZZ

Sample Output 4

No

Problem Statement

Takahashi is a cashier.

There is a cash register with 11 keys: 00, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The cash register initially displays 0. Whenever he types the key 00, the displayed number is multiplied by 100; whenever he types one of the others, the displayed number is multiplied by 10, and then added by the number written on the key.

Takahashi wants the cash register to display an integer S. At least how many keystrokes are required to make it display S?

Constraints

• 1\leq S\leq 10^{100000}
• S is an integer.

Sample Input 1

40004

Sample Output 1

4

For example, the following four keystrokes make the cash register display 40004. Initially, the cash register displays 0.

• Type the key 4. It now displays 4.
• Type the key 00. It now displays 400.
• Type the key 0. It now displays 4000.
• Type the key 4. It now displays 40004.

He cannot make it display 40004 with three or fewer keystrokes, so 4 should be printed.

Sample Input 2

1355506027

Sample Output 2

10

Sample Input 3

10888869450418352160768000001

Sample Output 3

27

Note that S may not fit into a 64-\operatorname{bit} integer type.

Problem Statement

There are N people in an xy-plane. Person i is at (X_i, Y_i). The positions of all people are different.

We have a string S of length N consisting of L and R.
If S_i = R, Person i is facing right; if S_i = L, Person i is facing left. All people simultaneously start walking in the direction they are facing. Here, right and left correspond to the positive and negative x-direction, respectively.

For example, the figure below shows the movement of people when (X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) =(4, 1), S = RRL.

We say that there is a collision when two people walking in opposite directions come to the same position. Will there be a collision if all people continue walking indefinitely?

Constraints

• 2 \leq N \leq 2 \times 10^5
• 0 \leq X_i \leq 10^9
• 0 \leq Y_i \leq 10^9
• (X_i, Y_i) \neq (X_j, Y_j) if i \neq j.
• All X_i and Y_i are integers.
• S is a string of length N consisting of L and R.

Sample Input 1

3
2 3
1 1
4 1
RRL

Sample Output 1

Yes

This input corresponds to the example in the Problem Statement.
If all people continue walking, Person 2 and Person 3 will collide. Thus, Yes should be printed.

Sample Input 2

2
1 1
2 1
RR

Sample Output 2

No

Since Person 1 and Person 2 walk in the same direction, they never collide.

Sample Input 3

10
1 3
1 4
0 0
0 2
0 4
3 1
2 4
4 2
4 4
3 3
RLRRRLRLRR

Sample Output 3

Yes

Problem Statement

You are given a sequence of non-negative integers A=(a_1,a_2,\ldots,a_N).

Let S be the set of non-negative integers that can be the sum of K terms in A (with distinct indices).

Find the greatest multiple of D in S. If there is no multiple of D in S, print -1 instead.

Constraints

• 1 \leq K \leq N \leq 100
• 1 \leq D \leq 100
• 0 \leq a_i \leq 10^9
• All values in the input are integers.

Sample Input 1

4 2 2
1 2 3 4

Sample Output 1

6

Here are all the ways to choose two terms in A.

• Choose a_1 and a_2, whose sum is 1+2=3.
• Choose a_1 and a_3, whose sum is 1+3=4.
• Choose a_1 and a_4, whose sum is 1+4=5.
• Choose a_2 and a_3, whose sum is 2+3=5.
• Choose a_2 and a_4, whose sum is 2+4=6.
• Choose a_3 and a_4, whose sum is 3+4=7.

Thus, we have S=\{3,4,5,6,7\}. The greatest multiple of 2 in S is 6, so you should print 6.

Sample Input 2

3 1 2
1 3 5

Sample Output 2

-1

In this example, we have S=\{1,3,5\}. Nothing in S is a multiple of 2, so you should print -1.